Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 21 стр.

UptoLike

ВУЗ: 

КФУ | Казань

Составители: 

Рубрика: 

∗ : F × F → F (F, +) (F \ {0}, ∗)
R
m
F
2
0 1 0+0 = 0 0+1 = 1 1+1 = 0 0∗0 = 0 0∗1 = 0 1∗1 = 1
A
3
(F
2
)
0 1
V
n
(C) = (V, +, ·)
n · : C × V → V
V ·
0
= ·|R : R × V → V
V
V
R
2n
= (V, +, ·
0
)
2n
{e
k
} k = 1, . . . , n V
n
(C) 2n
{e
k
, ie
k
} k = 1, . . . , n
a
k
e
k
+ b
k
(ie
k
) = 0 =⇒ (a
k
+ ib
k
)e
k
= 0 =⇒
a
k
+ ib
k
= 0 ∈ C k = 1, . . . , n =⇒ a
k
, b
k
= 0 ∈ R k = 1, . . . , n
v = v
k
e
k
v
k
∈ C =⇒ v = (a
k
+ ib
k
)e
k
v
k
= a
k
+ ib
k
=⇒
v = a
k
e
k
+ b
k
(ie
k
)
V
R
2n
= (V, +, ·
0
)
V
n
(C) = (V, +, ·)
A
R
2n
= (A, V
R
2n
, ψ)
A
n
(C) = (A, V
n
(C), ψ)
A
2
(C)
∗ : F×F → F         7510*  )7- (F, +) F 1-::27570B,58 932..5 (F \ {0}, ∗) F
1-::27570B,58 932..5 0 2:,-“*,0* D0/730+270B,- .- -7,-‰*,0‡ 1 /6-“*
,0‡ < ’30 ¨7-: /-C35,8‡7 /:A/6 7510* .-,8708  BB*D*,,A* 35,** D68 5„
„0,,-9- .3-/735,/7B5 ,5D .-6*: R  151 60,*”,58 E5B0/0:-/7> 0 ,*E5B0/0
:-/7> B*17-3-B  +5E0/  3*.*3  1--3D0,57A  .-D.3-/735,/7B-  m .6-/1-/7> 
60,*”,-* -7-+35“*,0*  5„„0,,-* -7-+35“*,0* <
   ªœZœ«œ ––^ /75710 -7 D*6*,08 ,5 G -+35E2‡7 .-6* F  /-/7-8ˆ** 0E DB2C
¨6*:*,7-B 0 0 1 •0 + 0 = 0  0 + 1 = 1  1 + 1 = 0  0 ∗ 0 = 0  0 ∗ 1 = 0  1 ∗ 1 = 1‹<
                                                               2


  -15E57>  )7- 73*C:*3,-* 5„„0,,-* .3-/735,/7B- A3(F2) /-/7-07 0E º :0
¨6*:*,7-B 0 ,5”70 B/* .38:A* 0 B/* .6-/1-/70 ¨7-9- .3-/735,/7B5<
   ҙœ¤œ\]Y^ -/.-6>E-B57>/8 7*: )7- 15“D58 0E 73*C 1--3D0,57 7-)10
060 B*17-35 :-“*7 .30,0:57> 3-B,- DB5 E,5)*,08 0 0 1 <
   ŽXYZ[—¡Y\]Y^ž}hi‚ V (C) = (V, +, · ) Ÿ vgdeomvhbgm kmvigfbgm efgp
hifjbhikg fjldmfbghia n w xnm · : C × V → V Ÿ gemfj†at }dbgymp
                                  n


bat zomdmbigk al V bj vgdeomvhbcm sahojw a ·0 = · | R : R × V → V
Ÿn gemfj†at }dbgymbat zomdmbigk al V bj kmqmhikmbbcm sahoj€ ¢gp
x j V2n
      R                                           v
          = (V, +, ·0 ) Ÿ kmqmhikmbbgm km igfbgm efghifjbhikg fjldmf p
bghia 2n €
   £—™œ¤œšY[¥˜š›—^ /60 {e }  k = 1, . . . , n F +5E0/ B V (C)  7- 2n B*1
7-3-B {ek , iek }  k = 1, . . . , n 60,*”,- ,*E5B0/0:A / B*ˆ*/7B*,,A:0 1-¨„
                                    k                               n

„0½0*,75:0 < *”/7B07*6>,-  ak e + bk (ie ) = 0 =⇒ (ak + ibk )e = 0 =⇒
ak + ibk = 0 ∈ C  k = 1, . . . , n  =⇒ ak , bk = 0 ∈ R  k = 1, . . . , n < ’30
                                        k        k                          k


¨7-: v = vk ek  vk ∈ C =⇒ v = (ak + ibk )ek  9D* vk = ak + ibk =⇒
v = ak ek + bk (iek ) < 
   VWXYZY[Y\]Y^ ¹mvigfbgm efghifjbhikg VR = (V, +, ·0 ) bjlckjmiht
gkmqmhikombamd vgdeomvhbgxg kmvigfbgxg efghifjbhikj Vn(C) = (V, +, · ) €
                                                       2n


   _``abbgm efghifjbhikg AR2n = (A, V2n         R
                                                   , ψ) bjlckjmiht gkmqmhikombap
md vgdeomvhbgxg j``abbgxg efghifjbhikj An(C) = (A, Vn(C), ψ) €
   ’*3*C-D 1 -B*ˆ*/7B6*,08: .-EB-68*7 /)0757>  )7- 1-:.6*1/,A* B*17-3
,A* 0 5„„0,,A* .3-/735,/7B5 8B68‡7/8 -D,-B3*:*,,- 0 B*ˆ*/7B*,,A:0
B*17-3,A:0 0 •/--7B*7/7B*,,-‹ 5„„0,,A:0 .3-/735,/7B5:0 <
   ŽX]YX^ ’2/7> B 1-:.6*1/,-: 5„„0,,-: .3-/735,/7B* A (C) B •1-:
                                                                        2

                                         ©Õ

Страницы